A general theory for the elastic design of a compound cylinder made by shrinking together many concentric cylinders is described. Each cylinder may have entirely different strength and operate at any temperature under any pressure, internal or external. The only assumptions, in addition to the usual homogeneity and isotropy in each member, are that they have the same Young’s modulus, although even different elastic moduli could be accommodated, and that they are not so thin that stability becomes a problem.

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